Other than the aforementioned technical complexity in inverting the Gram matrix,
there is another delicate point about the Lorentz tensor decomposition approach in D dimensions,
as already briefly mentioned above.
In cases where the external state consists only of bosons, a list of fixed number of Lorentz tensor structures
is indeed linearly complete in D dimensions to all orders in perturbation theory [1]}, [2]}.
However, if there are external fermions involved in the scattering, the complete and linearly independent set of basis
structures will generally increase with the perturbative order at which the scattering amplitude is computed,
because the Dirac algebra is formally infinite dimensional in non-integer D dimensions, as discussed
for the four-quark scattering amplitude \(q \bar{q} \rightarrow Q\bar{Q}\)  in [3]}, [4]}.
Of course, at each given perturbative order only a finite number of linearly
independent Lorentz structures can appear in an amplitude, because the corresponding Feynman diagrams are
just a set of finite elements. These additional D-dimensional Lorentz structures
are either evanescent by themselves or will lead to additional evanescent structures of
the same number computed by the procedure discussed above.
